EE 495 Modern Navigation Systems Inertial Sensor Errors Friday, Feb 19 EE 495 Modern Navigation Systems

Inertial Sensor Errors Inertial Sensor Modeling - Terminology Accuracy: Proximity of the measurement to the true value Precision: The consistency with which a measurement can be obtained Resolution: The magnitude of the smallest detectable change. Sensitivity: The ratio between the change in the output signal to a change in input physical signal. Slope of the input-output fit line. Linearity: The deviation of the output from a “best” straight line fit for a given range of the sensor Akin to the mean Akin to the standard deviation Friday, Feb 19 EE 495 Modern Navigation Systems

EE 495 Modern Navigation Systems Inertial Sensor Errors Inertial Sensor Modeling – Accuracy vs Precision Accurate but not precise Neither accurate nor precise Precise but not accurate Both accurate and precise Friday, Feb 19 EE 495 Modern Navigation Systems

Inertial Sensor Errors Inertial Sensor Modeling – Error Sources Bias – Often the most critical error source Fixed Bias Deterministic in nature and can be addressed by calibration Often modeled as a function of temperature Bias Stability Varies from run-to-run as a random constant Bias Instability In-run bias drift – Typically modeled as a random walk Gyro bias errors are a major INS error source Friday, Feb 19 EE 495 Modern Navigation Systems

Inertial Sensor Errors Inertial Sensor Modeling – Error Sources Scale Factor (SF) Fixed Scale Factor Error Deterministic in nature and can be addressed by calibration Often modeled as a function of temperature Scale Factor Stability 𝑠 𝑎 (accel) or 𝑠 𝑔 (gyro) Varies from run-to-run as a random constant Typically given in parts-per-million (ppm) Ref: Park, 04 Input Output True Measured Scale Factor Error The scale factor represents a linear approximation to the steady-state sensor response over a given input range – True sensor response may have some non-linear characteristics Friday, Feb 19 EE 495 Modern Navigation Systems

Inertial Sensor Errors Inertial Sensor Modeling – Error Sources Misalignment Refers to the angular difference between the ideal sense axis alignment and true sense axis vector A deterministic quantity typically given in milliradians Combining Misalignment & Scale Factor Normalized z-sense axis z-sense axis Friday, Feb 19 EE 495 Modern Navigation Systems

Inertial Sensor Errors Inertial Sensor Modeling – Error Sources Cross-Axis Response Refers to the sensor output which occurs when the device is presented with a stimulus which is vectorially orthogonal to the sense axis Misalignment and cross-axis response are often difficult to distinguish – Particularly during testing and calibration activities Friday, Feb 19 EE 495 Modern Navigation Systems

Inertial Sensor Errors Inertial Sensor Modeling – Error Sources Other noise sources Typically characterized as additive in nature May have a compound form White noise Gyros: White noise in rate  Angle random walk Accels: White noise in accel  Velocity random walk Quantization noise May be due to LSB resolution in ADC’s Flicker noise Colored noise A more detailed discussion of noise will be given at a later date Friday, Feb 19 EE 495 Modern Navigation Systems

Inertial Sensor Errors Inertial Sensor Modeling – Error Sources Gyro Specific Errors G-sensitivity The gyro may be sensitive to acceleration Primarily due to device mass assymetry Mostly in Coriolis-based devices (MEMS) G2-Sensitivity Anisoelastic effects Due to products of orthogonal forces The gyro may be sensitive to linear vibration!!!! Friday, Feb 19 EE 495 Modern Navigation Systems

Inertial Sensor Errors Inertial Sensor Modeling – Error Sources Accelerometer Specific Errors Axis Offset The accel may be mounted at a lever-arm distance from the “center” of the Inertial Measurement Unit (IMU) Leads to an “2r” type effect The accelerometer may be sensitive to angular rates!!!! Friday, Feb 19 EE 495 Modern Navigation Systems

Inertial Sensor Errors Inertial Sensor Modeling – Sensor Models Accelerometer measurement model Gyro measurement Model Typically, each accel/gyro measures along a single sense axis requiring three of each to measure the 3-tupple vector Friday, Feb 19 EE 495 Modern Navigation Systems

Inertial Sensor Errors Inertial Sensor Modeling – Applications Accelerometer Application Areas Ref: “INS/GPS Technology Trends“ by George T. Schmidt RTO-EN-SET-116(2010) Friday, Feb 19 EE 495 Modern Navigation Systems

Inertial Sensor Errors Inertial Sensor Modeling – Applications Gyro Application Areas Earth Rate Ref: “INS/GPS Technology Trends“ by George T. Schmidt RTO-EN-SET-116(2010) Friday, Feb 19 EE 495 Modern Navigation Systems

Inertial Sensor Errors Inertial Sensor Modeling – Applications Cost as a function of Performance and technology Different “Grades” of Inertial Sensors Ref: INS Tutorial, Norwegian Space Centre, 2008.06.09 Friday, Feb 19 EE 495 Modern Navigation Systems

Inertial Sensor Errors Inertial Sensor Modeling – SoA in MEMS Inertial Friday, Feb 19 EE 495 Modern Navigation Systems